Generalized Hadamard Matrices and Generalized Hadamard Graphs

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Quasi-Cyclic Generalized Hadamard Matrices

In this paper, we define quasi-cyclic(QC) generalized Hadamard matrices and balanced QC generalized Hadamard matrices. Then we propose a new construction method for QC generalized Hadamard matrices. The proposed matrices are constructed from the balanced optimal low correlation zone(LCZ) sequence set which has correlation value −1 within low correlation zone.

Expanding generalized Hadamard matrices over Gm by substituting several generalized Hadamard matrices over G

Over an additive abelian group of order and for a given positive integer , a generalized Hadamard matrix is defined as a matrix , where and , such that every element of appears exactly times in the list , , , , for any . In this paper, we propose a new method of expanding a over by replacing each of its -tuple with where . We may use (not necessarily all distinct) ’s for the substitution and th...

Tri-weight Codes and Generalized Hadamard Matrices

The existence is shown of a set of (p~ -1) generalized Hadamard matrices H(p, p~'~) of order p2'~, each of which is symmetric and regular. When normalized to become unitary matrices, they form a multiplicative group of order p'~, simply isomorphic to the additive group of GF(pm). The rows of these (p~ 1) matrices are shown to be the image, under the well-known isomorphic mapping relating the pt...

On generalized Hadamard matrices of minimum rank

Generalized Hadamard matrices of order qn−1 (q a prime power, n ≥ 2) over GF (q) are related to symmetric nets in affine 2-(qn, qn−1, (qn−1 − 1)/(q − 1)) designs invariant under an elementary abelian group of order q acting semi-regularly on points and blocks. The rank of any such matrix over GF (q) is greater than or equal to n− 1. It is proved that a matrix of minimum q-rank is unique up to a...